Computation-free preconditioners for the parallel solution of power system problems

Solution of a set of linear equations Ax=b is a recurrent problem in power system analysis. Because of computational dependencies, direct methods have proven to be of limited value in both parallel and highly vectorized computing environments. The preconditioned conjugate gradient method has been suggested as a better alternative to direct methods. The preconditioning step itself is not particularly well suited to parallel processing. Partitioned inverse representations of A are better suited to high performance computation. However, obtaining the partitioned inverse matrices can be expensive. This paper describes two techniques for preconditioning based on the partitioned inverses where the preconditioner matrix is obtained directly from an incomplete factorization without the need for additional numerical computation. Experiments indicate a 50% reduction in solution time in a parallel environment.